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ball曲线
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  ball curves
     A recursive algorithm for conversion of Bézier curves and Said Ball curves is presented, which is based on unified representation of Bézier curves and Said Ball curves.
     根据 Bézier曲线与 Said- Ball曲线的统一表示 ,给出了 Bézier曲线与 Said- Ball曲线之间相互转换的递归算法
短句来源
     TWO NEW TYPES OF GENERALIZED BALL CURVES
     两类新的广义Ball曲线
短句来源
     Last but not least, generalized Ball curves of the Wang-Said type (WSGB curves) are introduced in Chapter four.
     第四章介绍Wang-Said型广义Ball曲线(WSGB曲线)的定义,此类曲线包括Wang-Ball曲线、Said-Ball曲线及另外若干条中间曲线,以及它们的递归算法。
短句来源
     Ball curves were investigated extensively in polynomial spaces and applied in CAD systems.
     Ball曲线在多项式空间中得到了广泛的研究,而且在CAD系统中也有着广泛应用.
短句来源
     THE ALGORITHMS FOR EVALUATING TWO NEW TYPES OF GENERALIZED BALL CURVES/SURFACES AND THEIR APPLICATIONS
     两类新的广义Ball曲线曲面的求值算法及其应用
短句来源
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  ball curve
     BALL CURVE OF HIGH DEGREE AND ITS GEOMETRIC PROPERTIES
     高次Ball曲线及其几何性质
短句来源
     In this paper we construct composite cubic Ball curve to get G 2 continuity and the constructed curve is easier to control than the composite cubic Bezier curve.
     本文构造了组合三次Ball曲线达到G2 连续的过程并且构造出的曲线比组合三次B啨zier曲线更易控制 .
短句来源
     A class of cubic parameter curve of B-spline type is constructed in this paper with four arbitrary parameters, the cubic Hermite curve, Ball curve, Bezier curve, Timmer curve and B-spline curve as its special cases.
     构造了一类含四个参量的B样条型三次参数曲线,它以三次Hermite曲线、Ball曲线、Bezier曲线、Timmer曲线和B样条曲线为其特例。
短句来源
     By means of dual basis for Said Ball basis of even degree, we obtained Marsden identity and realized the conversion from Bézier curve to Said Ball curve These results are useful for the application of Said Ball curve and its popularization in Computer Aided Geometric Design
     利用任意偶数次Said Ball基的对偶基 ,给出Said Ball基函数下的Marsden恒等式 ,并实现B啨zier曲线到Said Ball曲线的转换 这些结果对Said Ball曲线在CAGD中的应用及推广是极为有益的
短句来源
     A class of cubic parameter curves are given. Hermite curve, Ball curve, Bezier curve and Timmer curve are its particular cases.
     给出了一类三次曲线,它以Hermite曲线、Ball曲线、Bezier曲线以及Timmer曲线为特例。
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  “ball曲线”译为未确定词的双语例句
     A new kind of Ball basis and curves in space K_n=span{1,t,t~2,\:,t~(n-1),sh t, ch t} are discussed.
     详细讨论了双曲混合多项式空间Kn=span{1,t,t2,…,tn-2,sht,cht}中的Ball基和Ball曲线.
短句来源
     The basis of space K_n, called H-Ball basis, is constructed based on H-Bézier basis, and then H-Ball curves are defined with this new basis.
     在H-Bézier基的基础上构造的一组新的基称为空间Kn的H-Ball基,用这组H-Ball基定义的曲线称为H-Ball曲线.
短句来源
     Degree Reduction of the Said-Ball Curves and Surfaces
     Said-Ball曲线曲面的降阶逼近
短句来源
     H-Ball curves could be applied for curves design and shape modeling in CAD systems and related fields.
     H-Ball曲线在CAD系统和相关领域的曲线设计和建模中得到了重要的应用.
短句来源
     This paper presents the fast subdivision algorithms for the Wang-Ball curve.
     本文首先介绍Wang-Ball曲线细分的快速算法;
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  ball curves
Unifying representation of Bézier curve and generalized ball curves
      
This paper presents two new families of the generalized Ball curves which include the Bézier curve, the generalized Ball curves defined by Wang and Said independently and some intermediate curves.
      


In the CONSURF system, developed by Ball, A.A. at the British Aircraft Corporation (Warton), the basis for curve is the following:[B3,0(u), B3,1(u), B3,2(u), B3,3(u)]= [(1-u)2, 2(1-u)2u, 2(1-u)u2, u2](0≤u≤1) (1)In this paper (1) is extended to the general forms, a series of geometric properties for Ball curve of n-th degree are derived, and its application prospect is indicated.

在由Ball,A.A.开发的英国飞机公司的CONSURF外形设计系统中,曲线的基函数定义为 [B_(3,0)(u),B_(3,1)(u),B_(3,2)(u),B_(3,3)(u)]=[(1-u)~2,2(1-u)~2u,2(1-u)u~2,u~2] (0≤u≤1) (1) 本文把(1)推广到一般形式,导出了n次Ball曲线的一系列几何性质,并指出了其应用前景。

In this paper, the necessary and sufficient condition and the sufficient condition for rational cubic Bezier curves representation of circular arcs are given. The similar results for rational cubic B-spline curves and Ball curves are presented.These algorithms are useful in shape design, numerical control and particularly in geometric modeling.

本文给出有理三次B(?)zier曲线r(t)=ω_0(1-t)~3r_0+3ω_1t(1-t)~2r_1+3ω_2t~2(1-t)r_2+ω_3t~3r_3/ω_0(1-t)~3+3ω_1t(1-t)~2+3ω_2t~2(1-t)+ω_3t~3 (0≤t≤1)精确地表示圆弧的充要条件和一个充分条件。对有理三次B样条曲线及Ball曲线也给出类似结果。这些算法对外形设计,数控技术特别对几何造型是有益的。

A class of cubic parameter curves are given. Hermite curve, Ball curve, Bezier curve and Timmer curve are its particular cases. Under certain conditions, this cubic parameter curves have the following properties: Convexity, retaining convex form, contact with the second edge of characteristic polygon and so on. This curve is different from Bezier curve, because its, shape can be changed after its characteristic polygon is given, so its shape can be changed according to our actual requirements.

给出了一类三次曲线,它以Hermite曲线、Ball曲线、Bezier曲线以及Timmer曲线为特例。这种参线曲线在一定条件下具有凸性、保凸性、与特征多边形第二边相切等性质。它克服了Bezier曲线在特征多边形给定之后就不能改变的缺点,可以根据实际需要调整曲线的形状。

 
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